It is often desirable to take repeated images of the Earth such that each image pixel is located at the exact same location on the Earth's surface. However, it is not possible to collect multiple images from the same exact location and with the same exact pointing angle. Resampling solves this problem by interpolating data samples from the original collection grid, which changes from image to image, to a grid that is fixed with respect to the Earth's surface. There are many other applications where resampling is used to determine signal values at desired locations that are different from those at which the data is collected.
In signal processing, downsampling is a process for reducing the sampling rate of a signal. This is usually done to reduce the data rate, or the size of the data. Downsampling is a special case of resampling. In a typical application, resampling and downsampling map data from one uniform grid to another uniform grid.
Downsampling is similar to resampling, except that the output grid has a sample spacing that is larger than the input grid spacing. The downsampling, however, needs to have a frequency response that is compatible with the output grid spacing, in order to minimize aliasing in the downsampled signal. This may be achieved by suppressing frequencies higher than the following:½αr 
where αr is the sample interval in the downsampled (or resampled) signal.
An example of downsampling is a reduced resampling by a factor of 2 relative to the resampled signal.
Imaging systems collect pixels on a collection grid that has approximately uniform angular spacing in the instrument's coordinate system. In many applications, it is desirable to map these pixels to a uniform geo-centric angular grid, such as latitude-longitude. The function that maps the collection sample grid to the Earth's surface is nonlinear. Accordingly, a uniform grid on the Earth's surface maps to a nonuniform grid in the instrument's coordinate system, and a uniform grid in the instrument's coordinate system maps to a nonuniform grid on the Earth's surface. Downsampling under these conditions presents two challenges, because the output grid spacing varies throughout the field-of-view (FOV). First, susceptibility to aliasing varies throughout the FOV. Second, the spatial resolution on the Earth's surface also varies throughout the FOV.
As will be described, the present invention addresses the above two challenges and provides a solution to each one.